60.1.541 problem 554

Internal problem ID [10555]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 554
Date solved : Sunday, March 30, 2025 at 06:01:16 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 40

ode:=x^(n-1)*diff(y(x),x)^n-n*x*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x^{n -1} \left (\frac {c_1 \left (\frac {x}{c_1}\right )^{\frac {1}{n}}}{x}\right )^{n}+n c_1 \left (\frac {x}{c_1}\right )^{\frac {1}{n}} \]

✓ Mathematica. Time used: 0.112 (sec). Leaf size: 54

ode=y[x] - n*x*D[y[x],x] + x^(-1 + n)*D[y[x],x]^n==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{y(x)=\frac {n x^2 K[1]-x^n K[1]^n}{x},x=c_1 (K[1]-n K[1])^{\frac {n}{1-n}}\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-n*x*Derivative(y(x), x) + x**(n - 1)*Derivative(y(x), x)**n + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0, _X0**n] 
No algorithms are implemented to solve equation _X0**n*x**(n - 1) - _X0*n*x + y(x)